Aguy wire to stabilize a transmitting tower 500 m high makes in angle of 50° with the ground. in a strong wind, the tower pulls the wire with a force of 1500.n. the anchorage of the wire is secure against any lateral pull, but it cannot withstand in an upward pull of more than 1200.n. does the wire come loose?

They give us the cable tension t = 1500 newton. We assume that the mass of the cable is negligible compared to that of the tower.

We have a force t of 1500 Newton. This force has a vertical component on the y axis and a horizontal component on the x axis.

Of these two components of force, we are especially interested in calculating is the magnitude of the vertical component.

If the angle that it forms with the ground is 50 °, then the vertical component of the force is:

Fy = 1500sin (50)

Fy = 1149 N. <1200 N

The wire will not be loose

no. dot product   =0 when vecs at right angles